Problem: Alice has a cute cat. To keep her cat fit, Alice wants to design an exercising walk for her cat! 

Initially, Alice's cat is located in a cell (x,y) of an infinite grid. According to Alice's theory, cat needs to move: 

  * exactly a steps left: from (u,v) to (u-1,v); 
  * exactly b steps right: from (u,v) to (u+1,v); 
  * exactly c steps down: from (u,v) to (u,v-1); 
  * exactly d steps up: from (u,v) to (u,v+1). 



Note that the moves can be performed in an arbitrary order. For example, if the cat has to move 1 step left, 3 steps right and 2 steps down, then the walk right, down, left, right, right, down is valid.

Alice, however, is worrying that her cat might get lost if it moves far away from her. So she hopes that her cat is always in the area [x_1,x_2]× [y_1,y_2], i.e. for every cat's position (u,v) of a walk x_1 ≤ u ≤ x_2 and y_1 ≤ v ≤ y_2 holds.

Also, note that the cat can visit the same cell multiple times.

Can you help Alice find out if there exists a walk satisfying her wishes?

Formally, the walk should contain exactly a+b+c+d unit moves (a to the left, b to the right, c to the down, d to the up). Alice can do the moves in any order. Her current position (u, v) should always satisfy the constraints: x_1 ≤ u ≤ x_2, y_1 ≤ v ≤ y_2. The staring point is (x, y).

You are required to answer t test cases independently.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^3) — the number of testcases. 

The first line of each test case contains four integers a, b, c, d (0 ≤ a,b,c,d ≤ 10^8, a+b+c+d ≥ 1).

The second line of the test case contains six integers x, y, x_1, y_1, x_2, y_2 (-10^8 ≤ x_1≤ x ≤ x_2 ≤ 10^8, -10^8 ≤ y_1 ≤ y ≤ y_2 ≤ 10^8).

Output

For each test case, output "YES" in a separate line, if there exists a walk satisfying her wishes. Otherwise, output "NO" in a separate line. 

You can print each letter in any case (upper or lower).

Example

Input


6
3 2 2 2
0 0 -2 -2 2 2
3 1 4 1
0 0 -1 -1 1 1
1 1 1 1
1 1 1 1 1 1
0 0 0 1
0 0 0 0 0 1
5 1 1 1
0 0 -100 -100 0 100
1 1 5 1
0 0 -100 -100 100 0


Output


Yes
No
No
Yes
Yes
Yes

Note

In the first test case, one valid exercising walk is $$$(0,0)→ (-1,0) → (-2,0)→ (-2,1) → (-2,2)→ (-1,2)→(0,2)→ (0,1)→ (0,0) → (-1,0)$$$

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;

public class c1 {
    public static void main(String[] args) {
        MyScanner scan = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

//        int t=1;
        int t=scan.nextInt();
        while(t-->0) {

            int[] arr=new int[4];
            int a=scan.nextInt(),b=scan.nextInt(),c=scan.nextInt(),d=scan.nextInt(),x=scan.nextInt(),y=scan.nextInt();
            for(int i=0;i<4;i++) arr[i]=scan.nextInt();
            int hor=b-a,ver=d-c;
            boolean hori=true,veri=true;

            if(x+hor>=arr[0]&&x+hor<=arr[2]) {
                if(a>b&&x-1<arr[0]) hori=false;
                else if (b>a&&x+1>arr[2]) hori=false;
                else if(a==b&&a!=0&&x+1>arr[2]&&x-1<arr[0]) hori=false;
                else hori=true;
            } else hori=false;
            if(y+ver>=arr[1]&&y+ver<=arr[3]) {
                if(c>d&&y-1<arr[1]) veri=false;
                else if (d>c&&y+1>arr[3]) veri=false;
                else if(d==c&&d!=0&&y+1>arr[3]&&y-1<arr[1]) veri=false;
                else veri=true;
            } else veri=false;

            out.println((veri&&hori)?"YES":"NO");
        }
        out.close();
    }

    //node
    static class Node implements Comparable<Node> {
        public int x,y;
        public Node(int x,int y) {
            this.x=x;
            this.y=y;
        }

        public int compareTo(Node other) {
            if(this.x==other.x) return 0;
            else if(this.x>other.x) return 1;
            else return -1;
        }

        public boolean equals(Node other) {
            return this.x==other.x;
        }

//        public int compareTo(Node other) {
//            if(this.y==other.y) return 0;
//            else if(this.y>other.y) return 1;
//            else return -1;
//        }
//
//        public boolean equals(Node other) {
//            return this.y==other.y;
//        }
    }
    //edge
    static class Edge implements Comparable<Edge> {
        public Node a,b;
        public int weight;

        public Edge(Node a,Node b,int weight) {
            this.a=a;
            this.b=b;
            this.weight=weight;
        }

        public int compareTo(Edge other) {
            if(this.weight==other.weight) return 0;
            else if(this.weight>other.weight) return 1;
            else return -1;
        }
    }

    //util
    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        if (a == 0)
            return b;
        return (a > b) ? gcd(a % b, b) : gcd(a, b % a);
    }

    public static int lcm(int a, int b) {
        return a * b / gcd(a, b);
    }

    public static int min(int a,int b) {
        if(a<=b) return a;
        else return b;
    }

    public static int max(int a,int b) {
        if(a>=b) return a;
        else return b;
    }

    public static int abs(int a) {
        if(a<0) return a*-1;
        else return a;
    }

    public static ArrayList<Integer> getPrimes(int n) {
        boolean prime[]=new boolean[n+1];
        Arrays.fill(prime,true);
        for (int p=2;p*p<=n;p++) {
            if (prime[p]) {
                for (int i=p*2;i<=n;i+=p) {
                    prime[i]=false;
                }
            }
        }
        ArrayList<Integer> primeNumbers=new ArrayList<Integer>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }

    public static boolean isPrime(int a) {
        if (a == 0 || a == 1) {
            return false;
        }
        if (a == 2) {
            return true;
        }
        for (int i = 2; i < Math.sqrt(a) + 1; i++) {
            if (a % i == 0) {
                return false;
            }
        }
        return true;
    }

    public static ArrayList<Integer> getDivisors(int n) {
        ArrayList<Integer> div = new ArrayList<Integer>();
        for (int i=1;i*i<=n;i++) {
            if (n%i==0) {
                div.add(i);
                if (n/i!=i)
                    div.add(n/i);
            }
        }
        return div;
    }

    //scanner
    public static PrintWriter out;

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}